Exponentials

Which equation describes the story below?

You start with $5 and triple your money every day.

• y=5(3)^x

• y=5^x

• y=5(3x)

• y=15^x

Tags

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Write an exponential function to model the situation. Then solve.

The cost of tuition at a college is $12,000 and is increasing at a rate of 6% per year. What will the cost be after 4 years?

• C(t) = 12000(1.06)^t ; $3149.72

• C(t) = 12000(.06)^t ; $3149.72

• C(t) = 12000(.06)^t ; $1472.95

• C(t) = 12000(1.06)^t ; $15149.72

Tags

CCSS.HSA.CED.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

A particular type of cell triples in number every hour. Which function can be used to find the number of cells present at the end of h hours if there are initially 6 of these cells?

• f(h) = 3(6)^h

• f(h) = 6x^h

• f(h) = 6(3)^h

• f(h) = 3(6h)

Tags

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

The amount of cola in a soda machine decreases by a rate of 5% each hour. The amount of cola in the machine was originally 75 gallons.

Which function models the amount of cola in gallons after h hours?

• f(h) = 75(-5)^h

• f(h) = -5(75)^h

• f(h) = .95(75)^h

• f(h) = 75(.95)^h

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

The function y = 24,220 (0.85)^x represents Mr. Bittle's investment in the stock exchange where x is measured in months.

Which statement is NOT true.

• Mr. Bittle loses 85% of his investment monthly

• Mr. Bittle initially invested $24,220

• Each month Mr. Bittle loses 15% of his investment

Tags

CCSS.HSA.SSE.A.1

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.IF.B.4

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

Write an exponential function to model the situation. You invest $1500. Your investment increases at a rate of 3.5%.

• B(t) = 1500(0.965)^t

• B(t) = 1500(1.035)^t

• B(t) = 1500(.035)^t

• B(t) = 1500(1.965)^t

Tags

CCSS.HSA.CED.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

Write an exponential function to model the situation. The value of a car is $18000 and is depreciating at a rate of 12% per year.

• V(t) = .88(18000)^t

• V(t) = .12(18000)^t

• V(t) = 18000(.88)^t

• V(t) = 18000(.12)^t

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

What is the a-value (or y-intercept) for the function: f(x) = 800(0.85)^x?

• 800

• 0.85

• 0.15

• x

Tags

CCSS.HSF.IF.A.2

CCSS.HSF.IF.B.4

What is the decay rate for the function: f(x) = 800(0.85)^x?

• 800

• 0.85

• 15%

• x

Tags

CCSS.HSA.SSE.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.B.5

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation that models this situation?

• y = 8(15,000)^x

• y = 15,000(1.08)^x

• y = 15,000(0.92)^x

• y = 15,000(0.08)^x

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5